Were any signers of the Declaration of Independence, Articles of Confederation, or Constitution of the United States Black (also called Negro)?

The population data that you quote in the question derived from a series of censuses taken in the thirteen colonies by the British government, and the early governments of the United States after the Revolutionary War. The population estimates based on data from censuses taken during the colonial period are, to say the least, generally accepted to be less reliable than we would like. There are a number of reasons for this, some of which are discussed in this paper on Population in the Colonial & Continental Periods.

Some returns survive for the early period. Most, unfortunately, do not. A list of known surviving returns can be found on the FamilySearch Wiki.

However, these censuses are the basis for the racial and ethnic demographics that you cite in the question, and they, together with their successors, the 1790 and 1800 United States Federal Census are the obvious primary source documents with which to answer your questions.

Your first question asks:

Is there any primary source evidence that any Black (also called Negro) was a signer of the United States Declaration of Independence, Articles of Confederation, or Constitution of the United States?

The answer to this is no.

It is a relatively straightforward - if time-consuming - matter to make list of the individuals who signed those documents, and then locate their census return in the 1790 or 1800 census. These returns are preserved by the US National Archives, but have been digitised and indexed by a number of family history sites, including FamilySearch (The records are available free-of-charge on FamilySearch. You may need to pay to view them on other sites, or visit a library where those sites may also be available for free).

Alexander Hamilton

Now, there have been a number of claims in recent years that Alexander Hamilton may have been black, or at least of mixed race. Hamilton was certainly illegitimate. There is undoubtedly a question over the identity of his father. Newspaper reports and other records show that his political enemies certainly made statements implying that Hamilton was of mixed race. The argument is set out concisely in this article Was Alexander Hamilton Black?

So what does the evidence say?

Well, a quick check of the 1790 and 1800 US federal census records on FamilySearch identifies 14 heads of household named Alexander Hamilton. None of the individuals self-identified as anything other than "white". (We know that Hamilton was practising in New York in 1800).

So the primary source evidence states that Hamilton was white.

A further claim that Hamilton was of mixed-race rests on a series of DNA tests carried out on 4 descendants of Hamilton's grandson, John C. A. Hamilton.

These tests were part of a wider study of the Hamilton surname, and so were limited to the Y-chromosome. The Y-chromosome is passed from father to son. Allowing for mutations which appear over time, the male line in a family all inherit identical copies of this chromosome from their fathers. The analysis

"... strongly indicates that there has been no non-paternal event in either of their lines since John C. A., the grandson of Alexander [Hamilton]".

Therefore, assuming that Hamilton was actually the father of his son, and that his son was actually the father of John C. A. Hamilton (i.e. no 'non-parental events' occurred), the Y-chromosome evidence recorded by the study is essentially identical to the chromosome Hamilton inherited from his father (whoever his father actually was).

The results of that study are presented and discussed by the project co-ordinator Gordon Hamilton. The page includes a link to the data underpinning their results and discussion, presented in tabular form.

Now, two participants of that study inherited haplogroup E which:

".. is an African haplogroup but it occurs to a small extent in Europe and Britain, possibly arriving in the latter during Roman times."

(In fact, the Y-chromosome haplogroups that most commonly appear in populations that originated in sub-Saharan Africa are A, B2a1a, E1a, E1b1, E2. These haplogroups, together with sub-haplogroups are generally accepted to be evidence of sub-Saharan African ancestry. Only the E-1 group was reported in the Hamilton surname study).

This the fact that these 2 individuals inherited haplogroup E is sometimes presented as "evidence that Alexander Hamilton had African ancestry". Unfortunately, it can be easily demonstrated that this claim is nonsense.

Participants in the study are identified by codes, rather than by name, to protect their identities. The two participants in the study who inherited haplogroup E-1 are identified by the codes H-271 & H-308. The discussion notes that these individuals are second-cousins, and so it is unsurprising that they share the Y-chromosome.

However, these were not the same individuals as the 4 descendants of John Hamilton (who are identified as H-039, H-073, H-079, and H-072).

There is thus absolutely no evidence for any African DNA in Hamilton's family tree from that data-set.

We can therefore say that there is no (presently known) primary source, or DNA evidence that suggests that Hamilton was black.

(Of course, none of that is likely to change people's minds. People often believe what they want to believe in cases like this. A point eloquently made by Robin Gane-McCalla in the article linked above).

Your second question asks:

Were the signers of the United States Declaration of Independence, Articles of Confederation, and Constitution of the United States each a White man?

Given that the division of the population in the demographics you cited in the question is essentially binary, in that it contained only two categories, then - based on the answer to your first question above - the answer here is clearly yes.

On the basis of known surviving evidence, the people who signed those documents were both white and male.

Should any primary source document surface that suggests any of those signatories was not white (or not male!), I suspect that would be front-page news in most news media around the world, and certainly in every history journal/magazine that covers the period!